Abstract

A single-mode-waveguide optical isolator based on propagation direction dependent cut-off frequency is proposed. The isolation bandwidth is the difference between the cut-off frequencies of the lowest forward and backward propagating modes. Perturbation theory is used for analyzing the correlation between the material distribution and the bandwidth. The mode profile determines an appropriate distribution of non-reciprocal materials.

Figures (6)

Dispersion curves of the proposed optical waveguide isolator. Solid lines are the lowest and second lowest modes. Dashed lines indicate forward and backward propagating modes for Δε≠0. Only one forward wave is guided within the isolation range Δω̄.

Optical isolator structures: (a,b) right-left configuration, (c,d) up-down configuration, (e) rib waveguide, and (f) trapezoidal configuration. C is a low-index material, A is a reciprocal material, and B is non-reciprocal material. B+ and B- have anti-parallel magnetizations. The magnetization direction in each non-reciprocal material is indicated by the single-ended arrows.

(a). Dispersion curves of the optical isolator in Fig. 2(b). where w/a=0.4 and h/a=0.3. The value a is the scaling length. The permittivity tensors are ε0 [12.25 0 0; 0 12.25∓i; 0 ±i 12.25] for B+ and B-. The substrate C is isotropic (ε=2.13ε0) where ε0 is the permittivity of vacuum. We have selected large off-diagonal values so that isolation is clearly shown. (b) Electric field component profiles of the lowest TE and TM modes at |β|a/2π=0.8 for forward and backward directions. “A on C” represents a reciprocal waveguide (Δε=0)-the unperturbed case. “B+B- on C” shows a nonreciprocal isolator waveguide (the perturbed case with magnetic material). The modal field changes are negligible even due to large perturbation, so using perturbation theory is justified.